This computational model of a spherical thermoplastic sample burning in microgravity separates the
solution of the energy equation, for which material properties are treated in bulk as purely radial functions,
from the calculations of the transport of mass through the polymer melt by means of individual
bubbles. This section describes the application of the equations and approaches developed in the Theory
section above to the calculations of the evolution of the heated polymeric sphere.
A flowchart outlining the procedure followed at each timestep is presented in Figure
5. The calculations
to be described are:
Mass balance: Given the temperature field, compute the total amount of gas generated in each
element.
Bubble growth: Divide the gas among the bubbles within each element and calculate the new
radius and growth rate of each bubble.
Bubble migration: Use the radius, growth rate, distance from the surface, and local material properties
of the polymer melt to determine the velocity of each bubble and locate its final position
after this timestep.
Bubble merging: If bubbles overlap, combine them.
Bubble bursting: Determine which bubbles have satisfied the requirements for bursting at the
sample surface and subtract these gases from the total mass of the sample; determine the resulting
mass loss rate.
Bubble distribution within elements: For bubbles remaining within the sample, determine the
elements to which each contributes.
Bubble nucleation: Nucleate new bubbles, making sure each element contains at least one.
Bulk material properties: Calculate the volume fractions of gas and polymer within each element
and use this information to determine material properties.
Momentum equations: Consider the swelling due to gasification and shrinkage due to mass (and
volume) loss to calculate the radial velocities of gas, polymer, and elements.
Energy equation: Calculate the radial temperature field at the current timestep from the bulk
material properties of each element.
